TSTP Solution File: PUZ040-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ040-1 : TPTP v8.1.2. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:24:03 EDT 2023
% Result : Unsatisfiable 0.20s 0.65s
% Output : Proof 4.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ040-1 : TPTP v8.1.2. Bugfixed v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 23:13:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.65 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.65
% 0.20/0.65 % SZS status Unsatisfiable
% 0.20/0.65
% 3.72/0.84 % SZS output start Proof
% 3.72/0.84 Take the following subset of the input axioms:
% 3.72/0.85 fof(b_left, axiom, ![V1, V2, V3, V4, H, X, Y, S2, S3, S4, S1]: (~state(bb(X, s(Y)), V1, V2, V3, V4, H, S1, S2, S3, S4, e1(X, Y), e2(s(X), Y)) | state(bb(X, Y), V1, V2, V3, V4, H, S1, S2, S3, S4, e1(X, s(s(Y))), e2(s(X), s(s(Y)))))).
% 3.72/0.85 fof(goal_state, negated_conjecture, ![E2, E1, V1_2, V2_2, V3_2, H2, S2_2, S3_2, S4_2, S1_2, V4_2]: ~state(bb(o, o), V1_2, V2_2, V3_2, V4_2, H2, S1_2, S2_2, S3_2, S4_2, E1, E2)).
% 3.72/0.85 fof(h_right, axiom, ![B, V1_2, V2_2, V3_2, X2, Y2, S2_2, S3_2, S4_2, E2_2, S1_2, V4_2]: (~state(B, V1_2, V2_2, V3_2, V4_2, h(X2, Y2), S1_2, S2_2, S3_2, S4_2, e1(X2, s(s(Y2))), E2_2) | state(B, V1_2, V2_2, V3_2, V4_2, h(X2, s(Y2)), S1_2, S2_2, S3_2, S4_2, e1(X2, Y2), E2_2))).
% 3.72/0.85 fof(initial_state, hypothesis, state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), o), e2(s(s(s(s(o)))), s(s(s(o)))))).
% 3.72/0.85 fof(s1_down, axiom, ![B2, V1_2, V2_2, V3_2, H2, X2, Y2, S2_2, S3_2, S4_2, E2_2, V4_2]: (~state(B2, V1_2, V2_2, V3_2, V4_2, H2, s1(X2, Y2), S2_2, S3_2, S4_2, e1(s(X2), Y2), E2_2) | state(B2, V1_2, V2_2, V3_2, V4_2, H2, s1(s(X2), Y2), S2_2, S3_2, S4_2, e1(X2, Y2), E2_2))).
% 3.72/0.85 fof(s1_left, axiom, ![B2, V1_2, V2_2, V3_2, H2, X2, Y2, S2_2, S3_2, S4_2, E2_2, V4_2]: (~state(B2, V1_2, V2_2, V3_2, V4_2, H2, s1(X2, s(Y2)), S2_2, S3_2, S4_2, e1(X2, Y2), E2_2) | state(B2, V1_2, V2_2, V3_2, V4_2, H2, s1(X2, Y2), S2_2, S3_2, S4_2, e1(X2, s(Y2)), E2_2))).
% 3.72/0.85 fof(s1_up, axiom, ![B2, V1_2, V2_2, V3_2, H2, X2, Y2, S2_2, S3_2, S4_2, E2_2, V4_2]: (~state(B2, V1_2, V2_2, V3_2, V4_2, H2, s1(s(X2), Y2), S2_2, S3_2, S4_2, e1(X2, Y2), E2_2) | state(B2, V1_2, V2_2, V3_2, V4_2, H2, s1(X2, Y2), S2_2, S3_2, S4_2, e1(s(X2), Y2), E2_2))).
% 3.72/0.85 fof(s3_up, axiom, ![B2, V1_2, V2_2, V3_2, H2, X2, Y2, S2_2, S4_2, E2_2, S1_2, V4_2]: (~state(B2, V1_2, V2_2, V3_2, V4_2, H2, S1_2, S2_2, s3(s(X2), Y2), S4_2, e1(X2, Y2), E2_2) | state(B2, V1_2, V2_2, V3_2, V4_2, H2, S1_2, S2_2, s3(X2, Y2), S4_2, e1(s(X2), Y2), E2_2))).
% 3.72/0.85 fof(swap_blanks, axiom, ![Q, W, B2, V1_2, V2_2, V3_2, H2, X2, Y2, S2_2, S3_2, S4_2, S1_2, V4_2]: (~state(B2, V1_2, V2_2, V3_2, V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(X2, Y2), e2(Q, W)) | state(B2, V1_2, V2_2, V3_2, V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(Q, W), e2(X2, Y2)))).
% 3.72/0.85 fof(v1_down, axiom, ![B2, V2_2, V3_2, H2, X2, Y2, S2_2, S3_2, S4_2, E2_2, S1_2, V4_2]: (~state(B2, v1(X2, Y2), V2_2, V3_2, V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(s(s(X2)), Y2), E2_2) | state(B2, v1(s(X2), Y2), V2_2, V3_2, V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(X2, Y2), E2_2))).
% 3.72/0.85 fof(v3_down, axiom, ![B2, V1_2, V2_2, H2, X2, Y2, S2_2, S3_2, S4_2, E2_2, S1_2, V4_2]: (~state(B2, V1_2, V2_2, v3(X2, Y2), V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(s(s(X2)), Y2), E2_2) | state(B2, V1_2, V2_2, v3(s(X2), Y2), V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(X2, Y2), E2_2))).
% 3.72/0.85 fof(v3_right, axiom, ![B2, V1_2, V2_2, H2, X2, Y2, S2_2, S3_2, S4_2, S1_2, V4_2]: (~state(B2, V1_2, V2_2, v3(X2, Y2), V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(X2, s(Y2)), e2(s(X2), s(Y2))) | state(B2, V1_2, V2_2, v3(X2, s(Y2)), V4_2, H2, S1_2, S2_2, S3_2, S4_2, e1(X2, Y2), e2(s(X2), Y2)))).
% 3.72/0.85 fof(v4_down, axiom, ![B2, V1_2, V2_2, V3_2, H2, X2, Y2, S2_2, S3_2, S4_2, E2_2, S1_2]: (~state(B2, V1_2, V2_2, V3_2, v4(X2, Y2), H2, S1_2, S2_2, S3_2, S4_2, e1(s(s(X2)), Y2), E2_2) | state(B2, V1_2, V2_2, V3_2, v4(s(X2), Y2), H2, S1_2, S2_2, S3_2, S4_2, e1(X2, Y2), E2_2))).
% 3.72/0.85
% 3.72/0.85 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.72/0.85 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.72/0.85 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.72/0.85 fresh(y, y, x1...xn) = u
% 3.72/0.85 C => fresh(s, t, x1...xn) = v
% 3.72/0.85 where fresh is a fresh function symbol and x1..xn are the free
% 3.72/0.85 variables of u and v.
% 3.72/0.85 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.72/0.85 input problem has no model of domain size 1).
% 3.72/0.85
% 3.72/0.85 The encoding turns the above axioms into the following unit equations and goals:
% 3.72/0.85
% 3.72/0.85 Axiom 1 (b_left): fresh41(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = true2.
% 3.72/0.85 Axiom 2 (v3_right): fresh6(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = true2.
% 3.72/0.85 Axiom 3 (h_right): fresh35(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 3.72/0.85 Axiom 4 (s1_down): fresh33(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 3.72/0.85 Axiom 5 (s1_left): fresh32(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 3.72/0.85 Axiom 6 (s1_up): fresh30(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 3.72/0.85 Axiom 7 (s3_up): fresh22(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 3.72/0.85 Axiom 8 (v1_down): fresh16(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 3.72/0.85 Axiom 9 (v3_down): fresh8(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 3.72/0.85 Axiom 10 (v4_down): fresh4(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = true2.
% 3.72/0.85 Axiom 11 (swap_blanks): fresh17(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2) = true2.
% 3.72/0.85 Axiom 12 (s1_down): fresh33(state(X, Y, Z, W, V, U, s1(T, S), X2, Y2, Z2, e1(s(T), S), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, W, V, U, s1(s(T), S), X2, Y2, Z2, e1(T, S), W2).
% 3.72/0.85 Axiom 13 (s1_left): fresh32(state(X, Y, Z, W, V, U, s1(T, s(S)), X2, Y2, Z2, e1(T, S), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, W, V, U, s1(T, S), X2, Y2, Z2, e1(T, s(S)), W2).
% 3.72/0.85 Axiom 14 (s1_up): fresh30(state(X, Y, Z, W, V, U, s1(s(T), S), X2, Y2, Z2, e1(T, S), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, W, V, U, s1(T, S), X2, Y2, Z2, e1(s(T), S), W2).
% 3.72/0.85 Axiom 15 (s3_up): fresh22(state(X, Y, Z, W, V, U, T, S, s3(s(X2), Y2), Z2, e1(X2, Y2), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, W, V, U, T, S, s3(X2, Y2), Z2, e1(s(X2), Y2), W2).
% 3.72/0.85 Axiom 16 (b_left): fresh41(state(bb(X, s(Y)), Z, W, V, U, T, S, X2, Y2, Z2, e1(X, Y), e2(s(X), Y)), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = state(bb(X, Y), Z, W, V, U, T, S, X2, Y2, Z2, e1(X, s(s(Y))), e2(s(X), s(s(Y)))).
% 3.72/0.85 Axiom 17 (h_right): fresh35(state(X, Y, Z, W, V, h(U, T), S, X2, Y2, Z2, e1(U, s(s(T))), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, W, V, h(U, s(T)), S, X2, Y2, Z2, e1(U, T), W2).
% 3.72/0.85 Axiom 18 (swap_blanks): fresh17(state(X, Y, Z, W, V, U, T, S, X2, Y2, e1(Z2, W2), e2(V2, U2)), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2) = state(X, Y, Z, W, V, U, T, S, X2, Y2, e1(V2, U2), e2(Z2, W2)).
% 3.72/0.85 Axiom 19 (v1_down): fresh16(state(X, v1(Y, Z), W, V, U, T, S, X2, Y2, Z2, e1(s(s(Y)), Z), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, v1(s(Y), Z), W, V, U, T, S, X2, Y2, Z2, e1(Y, Z), W2).
% 3.72/0.85 Axiom 20 (v3_down): fresh8(state(X, Y, Z, v3(W, V), U, T, S, X2, Y2, Z2, e1(s(s(W)), V), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, v3(s(W), V), U, T, S, X2, Y2, Z2, e1(W, V), W2).
% 3.72/0.85 Axiom 21 (v4_down): fresh4(state(X, Y, Z, W, v4(V, U), T, S, X2, Y2, Z2, e1(s(s(V)), U), W2), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2) = state(X, Y, Z, W, v4(s(V), U), T, S, X2, Y2, Z2, e1(V, U), W2).
% 3.72/0.85 Axiom 22 (v3_right): fresh6(state(X, Y, Z, v3(W, V), U, T, S, X2, Y2, Z2, e1(W, s(V)), e2(s(W), s(V))), true2, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = state(X, Y, Z, v3(W, s(V)), U, T, S, X2, Y2, Z2, e1(W, V), e2(s(W), V)).
% 3.72/0.86 Axiom 23 (initial_state): state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(o)), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), o), e2(s(s(s(s(o)))), s(s(s(o))))) = true2.
% 3.72/0.86
% 3.72/0.86 Goal 1 (goal_state): state(bb(o, o), X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = true2.
% 3.72/0.86 The goal is true when:
% 3.72/0.86 X = v1(s(s(o)), o)
% 3.72/0.86 Y = v2(o, s(s(s(o))))
% 3.72/0.86 Z = v3(s(s(s(o))), s(o))
% 3.72/0.86 W = v4(s(s(s(o))), s(s(s(o))))
% 3.72/0.86 V = h(s(s(o)), s(s(o)))
% 3.72/0.86 U = s1(s(s(s(s(o)))), o)
% 3.72/0.86 T = s2(s(s(s(o))), s(s(o)))
% 3.72/0.86 S = s3(s(s(o)), s(o))
% 3.72/0.86 X2 = s4(s(s(s(s(o)))), s(s(o)))
% 3.72/0.86 Y2 = e1(o, s(s(o)))
% 3.72/0.86 Z2 = e2(s(o), s(s(o)))
% 3.72/0.86
% 3.72/0.86 Proof:
% 3.72/0.86 state(bb(o, o), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(o, s(s(o))), e2(s(o), s(s(o))))
% 3.72/0.86 = { by axiom 16 (b_left) R->L }
% 3.72/0.86 fresh41(state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(o), o)), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.87 = { by axiom 18 (swap_blanks) R->L }
% 3.72/0.87 fresh41(fresh17(state(bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(o), o), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.87 = { by axiom 19 (v1_down) R->L }
% 3.72/0.87 fresh41(fresh17(fresh16(state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.87 = { by axiom 12 (s1_down) R->L }
% 3.72/0.87 fresh41(fresh17(fresh16(fresh33(state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), o), e2(o, o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.87 = { by axiom 18 (swap_blanks) R->L }
% 3.72/0.87 fresh41(fresh17(fresh16(fresh33(fresh17(state(bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(o, o), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.87 = { by axiom 19 (v1_down) R->L }
% 3.72/0.88 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.88 = { by axiom 12 (s1_down) R->L }
% 3.72/0.88 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), o), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.88 = { by axiom 22 (v3_right) R->L }
% 3.72/0.88 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(fresh6(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), s(o)), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(s(o))), o, v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.89 = { by axiom 15 (s3_up) R->L }
% 3.72/0.89 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(fresh6(fresh22(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s(s(o)), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(s(o))), o, v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.89 = { by axiom 13 (s1_left) R->L }
% 3.72/0.89 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(fresh6(fresh22(fresh32(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s(s(o)), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(s(o))), o, v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.90 = { by axiom 18 (swap_blanks) R->L }
% 3.72/0.90 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(fresh6(fresh22(fresh32(fresh17(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(o)), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(s(s(s(o)))), s(o), s(s(o)), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s(s(o)), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(s(o))), o, v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.90 = { by axiom 15 (s3_up) R->L }
% 3.72/0.90 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(fresh6(fresh22(fresh32(fresh17(fresh22(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(o))), s(o)), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s(s(s(o))), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(s(s(s(o)))), s(o), s(s(o)), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s(s(o)), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(s(o))), o, v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 3.72/0.91 = { by axiom 14 (s1_up) R->L }
% 3.72/0.91 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(fresh6(fresh22(fresh32(fresh17(fresh22(fresh30(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(o)), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), s(o), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s(s(s(o))), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(s(s(s(o)))), s(o), s(s(o)), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s(s(o)), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(s(o))), o, v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.41/0.92 = { by axiom 17 (h_right) R->L }
% 4.41/0.92 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(fresh6(fresh22(fresh32(fresh17(fresh22(fresh30(fresh35(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), s(s(s(o)))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), s(s(o)), s(o), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), s(o), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s(s(s(o))), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(s(s(s(o)))), s(o), s(s(o)), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s(s(o)), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(s(o))), o, v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.41/0.92 = { by axiom 21 (v4_down) R->L }
% 4.41/0.93 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(fresh6(fresh22(fresh32(fresh17(fresh22(fresh30(fresh35(fresh4(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(s(s(o)))), s(s(s(o)))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), s(s(o)), s(s(s(o))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), s(s(o)), s(o), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), s(o), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s(s(s(o))), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(s(s(s(o)))), s(o), s(s(o)), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s(s(o)), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(s(o))), o, v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.41/0.93 = { by axiom 18 (swap_blanks) R->L }
% 4.41/0.94 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(fresh6(fresh22(fresh32(fresh17(fresh22(fresh30(fresh35(fresh4(fresh17(state(bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e1(s(s(o)), o), e2(s(s(s(s(o)))), s(s(s(o))))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(o)), s(s(s(o)))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(s(o)), o, s(s(s(s(o)))), s(s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), s(s(o)), s(s(s(o))), h(s(s(o)), s(o)), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), s(s(o)), s(o), s1(s(s(s(o))), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), s(o), s2(s(s(s(o))), s(s(o))), s3(s(s(s(s(o)))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s(s(s(o))), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(o)), o)), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), s(o)), s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(s(s(s(o)))), s(o), s(s(o)), o), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(s(o))), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), o), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s(s(o)), s(o), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), s(o))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), s(s(s(o))), o, v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(o)), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o)))), true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.41/0.95 = { by axiom 20 (v3_down) R->L }
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% 4.41/0.95 = { by axiom 23 (initial_state) }
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% 4.41/0.96 = { by axiom 9 (v3_down) }
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% 4.41/0.97 = { by axiom 11 (swap_blanks) }
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% 4.41/0.97 = { by axiom 10 (v4_down) }
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% 4.41/0.98 = { by axiom 3 (h_right) }
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% 4.93/0.98 = { by axiom 6 (s1_up) }
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% 4.93/0.99 = { by axiom 7 (s3_up) }
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% 4.93/0.99 = { by axiom 11 (swap_blanks) }
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% 4.93/1.00 = { by axiom 5 (s1_left) }
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% 4.93/1.00 = { by axiom 7 (s3_up) }
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% 4.93/1.00 = { by axiom 2 (v3_right) }
% 4.93/1.00 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(fresh33(true2, true2, bb(o, s(o)), v1(o, o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(o)), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.93/1.00 = { by axiom 4 (s1_down) }
% 4.93/1.01 fresh41(fresh17(fresh16(fresh33(fresh17(fresh16(true2, true2, bb(o, s(o)), o, o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(s(s(s(s(o)))), o)), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.93/1.01 = { by axiom 8 (v1_down) }
% 4.93/1.01 fresh41(fresh17(fresh16(fresh33(fresh17(true2, true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(o))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), o, o, s(s(s(s(o)))), o), true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.93/1.01 = { by axiom 11 (swap_blanks) }
% 4.93/1.01 fresh41(fresh17(fresh16(fresh33(true2, true2, bb(o, s(o)), v1(s(o), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s(s(s(o))), o, s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.93/1.01 = { by axiom 4 (s1_down) }
% 4.93/1.01 fresh41(fresh17(fresh16(true2, true2, bb(o, s(o)), s(o), o, v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), e2(o, o)), true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.93/1.01 = { by axiom 8 (v1_down) }
% 4.93/1.01 fresh41(fresh17(true2, true2, bb(o, s(o)), v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))), s(o), o, o, o), true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.93/1.01 = { by axiom 11 (swap_blanks) }
% 4.93/1.01 fresh41(true2, true2, o, o, v1(s(s(o)), o), v2(o, s(s(s(o)))), v3(s(s(s(o))), s(o)), v4(s(s(s(o))), s(s(s(o)))), h(s(s(o)), s(s(o))), s1(s(s(s(s(o)))), o), s2(s(s(s(o))), s(s(o))), s3(s(s(o)), s(o)), s4(s(s(s(s(o)))), s(s(o))))
% 4.93/1.01 = { by axiom 1 (b_left) }
% 4.93/1.01 true2
% 4.93/1.01 % SZS output end Proof
% 4.93/1.01
% 4.93/1.01 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------